<div dir="ltr"><div class="gmail_default" style="font-family:verdana,sans-serif">Say X, Y, and Z are RVs. G is a sigma algebra.</div><div class="gmail_default" style="font-family:verdana,sans-serif"><br></div><div class="gmail_default" style="font-family:verdana,sans-serif">Z = X + Y</div><div class="gmail_default" style="font-family:verdana,sans-serif"><br></div><div class="gmail_default" style="font-family:verdana,sans-serif">If X and Y are both G-measurable, does this imply that Z is also G-measurable?</div><div class="gmail_default" style="font-family:verdana,sans-serif"><br></div><div class="gmail_default" style="font-family:verdana,sans-serif">I guess more generally - say a random variable is some function of other RVs. does the measurability of the two RVs that the function takes as inputs imply that the function itself is measurable with respect to that same sigma algebra?</div><div class="gmail_default" style="font-family:verdana,sans-serif"><br></div><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><font face="verdana, sans-serif">Richard Rosenbaum</font><div><font face="verdana, sans-serif">Master of Science in Computational Finance Candidate</font></div><div><font face="verdana, sans-serif">Carnegie Mellon University - Class of Dec. 2018</font></div></div></div></div></div>
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